The government said it was giving more money to tackle serious and organised crime and again announced an increase in counter-terrorism funding, which was first unveiled in the budget.

Early analysis suggests the extra money from central government will be swallowed up by extra pension costs forces will have to pay after a decision by the Treasury. That leaves money raised from local council taxes to fund extra costs from inflation. New funding for more officers or fighting crime will only then be available.

The home secretary, Sajid Javid, has previously accepted police were overstretched and needed more resources. That represented a reversal of the government’s stance that police were adequately funded, which had been the view first of Theresa May as home secretary and of her successor, Amber Rudd.

In a letter to Yvette Cooper, the chair of the home affairs committee, Javid said growing demands on officers meant the extra funding was necessary. “It is clear that demand pressures on the police have risen this year as a result of changing crime,” he said. “There has been a major increase in the reporting of high harm, previously hidden crimes such as child sexual exploitation and modern slavery. The challenge from serious and organised crime networks is growing.”

He continued: “Through the Serious Violence Strategy, we are bearing down on the worst spike in serious violence and knife crime that we have seen in a decade by combining support for more robust and targeted policing with effective long-term investment in prevention and earlier intervention.”

The Labour mayor of London, Sadiq Khan, said: “Londoners will be furious at the government’s announcement today. The additional funding represents a tiny fraction of the huge government cuts to the Met police since 2010 and will mean the number of police officers in London will continue to fall over the years ahead.”

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The West Midlands police and crime commissioner, David Jamieson, said his force needed £25.6m to avoid shrinking further, and the government had given only £15.9m. Jamieson said: “West Midlands Police has faced cuts of £175m since 2010, leading to over 2,000 police officers being lost during that period.

“Despite warm words over the last few months, this is once again a disappointing settlement that falls a long way short of what West Midlands police needed from the government.

“This government funding does not come anywhere near to covering what the force requires just to stand still. £25.6m is needed to cover extra pension costs, government-set pay increases and rising fuel costs this year.”

There was a warmer welcome from the National Police Chiefs’ Council lead for finance, chief constable Dave Thompson, who leads the West Midlands force. He said: “The additional funding through the police grant will help forces meet the costs of government pension changes and should allow chief constables and police and crime commissioners to avoid making further cuts.

“Increased flexibility through the council tax precept will give chief constables and police and crime commissioners the opportunity to address local issues – with many focusing on violent crime.”

Police forces needed at least £165m extra to pay for extra costs after the Treasury decided they needed to increase pension payments to meet a shortfall this year, rising to £417m next year.

The government said it was meeting that cost, but Labour said it was not.

Police chiefs were so angry about the extra pension charges they have decided to sue the government unless it backs down, an unprecedented decision.

Treasury’s budget claim to have provided £160m extra for counter-terrorism policing turned out to be a much smaller year-on-year increase of £59m, which the government confirmed again on Thursday.

More of the burden of paying for policing has switched from national government to local taxation.

Urban forces tend to be able to raise less per head for council tax than more rural areas. Urban forces such as the Metropolitan police, West Midlands, Greater Manchester and West Yorkshire forces rely more on central government grants for their funding than rural forces.